Shannon Dea

This paper considers Peirce's striking remarks about mathematics in a little-known review of Spinoza's Ethics within the larger context of his philosophy of mathematics. It argues that, for Peirce, true mathematical reasoning is always at the vanguard of thought, and resists logical demonstration. Through diagrammatic thought and her pre-theoretical innate faculty of logica utens, the great mathematician is able to see a theorem as true long before the logical apparatus necessary to demonstrate its truth exists. For Peirce, true mathematical thought is in some sense pre-logical, and thus, the logical demonstration of this thought in the form of mathematical proofs is in fact "merely a veil over the living thought."

In this paper, I elaborate affinities between Peirce, Spinoza and Royce, in order to illuminate the division between Peirce's and James's expressions of idealism. James contrasted Spinoza's and Royce's absolute idealism with his and Peirce's pluralistic idealism. I triangulate among Peirce, Spinoza and Royce to show that, contra James's view, Peirce himself was more at home in the absolutistic camp. In Section 2, I survey Peirce's discussions of Spinoza's pragmatism and of the divide within pragmatism Peirce perceived to obtain. In Section 3, I elaborate two early twentieth-century accounts of the idealistic division within pragmatism, and James's criticisms of absolute idealism in Spinoza and Royce. In Section 4, we turn our attention to Peirce's discussions of the absolute, and to the role of the absolute and the infinite in the thought of Spinoza, Royce and James. In the classification of pragmatist idealisms, I argue, James stands on one side; Peirce stands on the other with Roy..